When applying tape to sections of flexible material, a common problem with roll-type applicators is the formation of a wave in front of the applicator roll. An example of such a roll-type applicator is shown in U.S. Pat. No. 3,962,016, which relates to an applicator for taping the seam between thermoplastic synthetic resin foam sheets. Because of the flexibility of the sheets on which this apparatus rolls, and the weight of the apparatus carried by the applicator roll, the sheets tend to react to the pressure of any rolling by buckling upwardly in front of the roll, creating a wave. Then, when the tape is applied to such a wave in the sheet, there are apt to be air pockets between the tape and the sheet, through which liquid can seep.